What is the Greatest Common Factor of 49722 and 49728?

Greatest common factor (GCF) of 49722 and 49728 is 6.

GCF(49722,49728) = 6

We will now calculate the prime factors of 49722 and 49728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49722 and 49728.

How to find the GCF of 49722 and 49728?

We will first find the prime factorization of 49722 and 49728. After we will calculate the factors of 49722 and 49728 and find the biggest common factor number .

Step-1: Prime Factorization of 49722

Prime factors of 49722 are 2, 3, 8287. Prime factorization of 49722 in exponential form is:

49722 = 2¹ × 3¹ × 8287¹

Step-2: Prime Factorization of 49728

Prime factors of 49728 are 2, 3, 7, 37. Prime factorization of 49728 in exponential form is:

49728 = 2⁶ × 3¹ × 7¹ × 37¹

Step-3: Factors of 49722

List of positive integer factors of 49722 that divides 49722 without a remainder.

1, 2, 3, 6, 8287, 16574, 24861

Step-4: Factors of 49728

List of positive integer factors of 49728 that divides 49722 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 37, 42, 48, 56, 64, 74, 84, 96, 111, 112, 148, 168, 192, 222, 224, 259, 296, 336, 444, 448, 518, 592, 672, 777, 888, 1036, 1184, 1344, 1554, 1776, 2072, 2368, 3108, 3552, 4144, 6216, 7104, 8288, 12432, 16576, 24864

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49722 and 49728. The biggest common factor number is the GCF number.
So the greatest common factor 49722 and 49728 is 6.

Also check out the Least Common Multiple of 49722 and 49728